During the Dark Ages, following the Universe’s cooling to a point where atomic formation became possible, a shift occurred from an intensely hot and luminous environment to a cold and dark state. Over time, gravitational forces gradually amplified small perturbations in the distribution of gas, leading to the emergence of expansive voids and substantial hydrogen clouds (Peebles 1981). The 21-cm line, emitted through the hyperfine transition of neutral hydrogen, allows for the observation of how intervening hydrogen affects Cosmic Microwave Background (CMB) radiation at redshifted 21 cm wavelengths. Depending on whether the spin temperature of hydrogen is lower or higher than the CMB temperature, the 21-cm signal can manifest as slight absorption or emission, respectively, facilitating a detailed exploration of various epochs of the Universe. Observation of the 21-cm signal allows us to trace the distribution and density fluctuations of hydrogen clouds influenced by the underlying dark matter framework (Morales & Wyithe 2010). This methodology provides insights into the gravitational forces necessary for the aggregation of these clouds into protostellar bodies and contributes to our understanding of cosmic structure formation (Barkana 2016). By mapping variations in the 21-cm signal across different regions in the Dark Ages, we can infer the density and distribution of dark matter, shedding light on its role in catalysing the birth of the first stars and galaxies (Pritchard & Loeb 2012). Focusing on 21-cm cosmology not only enhances our understanding of dark matter’s influence on early star formation but also deepens our comprehension of the Universe’s evolutionary history during its most formative stages (Cohen et al. 2017).

The 21-cm hydrogen signal has been leveraged to provide constraints on cosmological parameters, contributing to our understanding of the Universe’s physical constants (Reis, Fialkov & Barkana 2020). Chen & Miralda-Escudé (2004) explored the impact of dark matter, dark energy, and baryonic physics on the 21-cm signal through simulations and theoretical analyses, highlighting its dependence on fundamental properties. Furlanetto, Oh & Briggs (2006) investigated the interplay of various processes during the Dark Ages and reionization, advancing our comprehension of the 21-cm signal’s evolution and enabling the estimation of cosmological parameters.

Observing the 21-cm signal faces significant challenges, primarily due to foreground contamination by galactic synchrotron radiation, extragalactic sources, and free–free emissions, which significantly overpower the target signal (Bernardi et al. 2010; Ghosh et al. 2012; Offringa et al. 2013; Barry et al. 2016; Lian et al. 2020). Ground-based observations, in particular, grapple with additional complications from the Earth’s ionosphere and terrestrial radio frequency interference (RFI), which distort and obscure the signal further (Lawrence, Little & Chivers 1964; Vedantham et al. 2013; Datta et al. 2016; Shen et al. 2021, 2022). Detecting the low-frequency 21-cm signal from the Dark Ages from Earth is particularly challenging due to the Earth’s ionosphere, which introduces substantial distortions and absorption effects at these frequencies. The ionosphere’s electron density fluctuations can cause signal propagation delays and scattering, distorting the 21-cm signal. Ground spillover, caused by the scattering and reflection of radio waves from the Earth’s surface, worsens the challenge, contributing to the overall noise floor and interfering with the cosmological signal, thereby limiting the sensitivity and precision of Earth-conducted observations. The strategic placement of a ground plane below the antenna is a common mitigation technique to address this issue (Singh et al. 2018; Mahesh et al. 2021; Cumner et al. 2022).

To address these challenges, calibration techniques and technological innovations have been developed through quantification of these phenomenons (Byrne et al. 2019; Shen et al. 2021). Despite the efforts of developing robust radiometers, the persistent issues of ionospheric distortion and terrestrial RFI underline the inherent limitations of ground-based observations (Offringa et al. 2013; Datta et al. 2016). This realization has spurred interest in alternative observation strategies, including the potential for space-based platforms. A pioneering approach involves deploying a satellite to orbit around the Moon, leveraging the Moon’s far side as a shield against Earth’s RFI and ionospheric effects, offering a clearer window to the cosmic 21-cm signal and a step forward in unraveling the mysteries of the Universe’s early epochs.

Earth-based low-frequency global signal experiments such as EDGES (Bowman, Rogers & Hewitt 2008), SARAS (Singh et al. 2018), LEDA (Bernardi et al. 2016), PRIZM (Philip et al. 2019), MIST (Monsalve et al. 2023), and REACH (de Lera Acedo et al. 2022) aim to constrain the physics of the cosmic dawn (CD) and the epoch of reionization (EoR). In contrast, earth-based interferometer radio experiments like LOFAR (van Haarlem et al. 2013), HERA (DeBoer et al. 2017), MWA (Tingay et al. 2013), and the future SKA Observatory (Bourke et al. 2015) are exploring the 21-cm signal to understand the early Universe’s spatial power spectrum. The EDGES experiment (Bowman et al. 2008), notable for its claim of detecting the global 21-cm signal at 78 MHz using two low-band dipole antennae operating between 50 and 100 MHz, has ignited a debate over its interpretation. This claim has been met with skepticism by other research groups amid concerns on the data analysis used (Hills et al. 2018; Sims & Pober 2019; Singh & Subrahmanyan 2019; Bevins et al. 2022).

Research into detecting the 21-cm signal from the dark ages is expanding, with missions such as LuSEE-Night (Bale et al. 2023), ROLSES (Burns et al. 2021b), and LCRT (Goel et al. 2022) focusing on surface single antenna observations, surface interferometry missions like FarView (Polidan et al. 2024), ALO (Klein Wolt, Falcke & Koopmans 2024), FARSIDE (Burns et al. 2021a), and LARAF (Chen et al. 2024), and interferometry in orbit such as DSL (Chen et al. 2021), along with single antenna in orbit missions like NCLE (Bentum et al. 2020), PRATUSH (Sathyanarayana Rao et al. 2023), and this work, CosmoCube, all concentrating on lunar-based observations. LuSEE-Night plans to utilize a lander with monopole antennas on the Moon’s far side, aiming for frequencies between 0.5 and 50 MHz. ROLSES has successfully landed, but the lander tipped over and ended up at a 30-deg angle to the horizontal (NASA Space Science Data Coordinated Archive 2024). While the four STACER antennas – spring-tensioned, collapsible antennas designed for deployment in space – were deployed, their exact final orientation remains uncertain. Nevertheless, the investigators confirm that data have been transmitted from the instrument and are now under analysis. The Chang’e 4 mission (Jia et al. 2018) also contributes with its rover equipped with antennas optimized for 40–80 MHz for one of its channels, demonstrating a trend towards more compact and efficient designs for lunar and space-based low-frequency signal detection (Lai et al. 2020). Proposed FarView, a lunar radio array mission, utilizes 100 000 dipole antennas, manufactured in situ on the Moon using metals extracted from the lunar regolith. Operating across a frequency range of 5 to 50 MHz, the array employs interferometry to enhance the resolution and depth of cosmic observations.

To investigate the cosmic dark ages and capture the significantly redshifted 21-cm hydrogen line, a robust radiometer is required, capable of detecting faint, low-frequency signals ranging from around 10 MHz at a redshift of 150 to approximately 45 MHz at a redshift of 30. This device integrates wideband design, employs low-noise amplification, and implements precise calibration techniques (Rogers & Bowman 2008), with long integration times essential for accumulating sufficient data for a detectable signal-to-noise ratio.

Building on this technological foundation, current experiments focus on redshifts from 6 to 28, targeting the EoR and CD. Our CosmoCube experiment aligns with the growing emphasis on lower frequencies, further extending the exploration of high redshifts, specifically targeting the range from 13 to 150 using a lunar orbiting CubeSat to detect the global 21-cm signal, as shown in Fig. 1. This approach not only promises insights into primordial fluctuations, non-Gaussian statistics deviations, and primordial gravitational waves but also reveals the cosmological model, dark matter properties, and the early Universe’s conditions through the intergalactic medium’s absorption against the CMB (Pritchard & Loeb 2012). Additionally, by being sensitive to electromagnetic energy injection, the Dark Ages’ 21-cm signal offers a novel way to investigate dark matter models and explore exotic physics beyond current constraints, aiming for significant improvements in data precision (Koopmans et al. 2021).

The study by Mondal, Barkana & Fialkov (2023) provides a precise methodology for probing exotic dark matter models through the analysis of the 21-cm signal from the dark ages, focusing on variations such as millicharged dark matter, dark matter with non-gravitational interactions, and dark matter decay. These models have the potential to significantly alter the thermal and ionization history of the early Universe. By analysing the power spectrum and global signal variations at high redshifts, models can be constrained, revealing how dark matter interacts with baryonic matter and impacts cosmic structure formation before the appearance of the first stars and galaxies. Although power spectrum analysis provides detailed insights into spatial variations and could reveal subtle dark matter influences, it requires complex observational setups. Due to simpler experimental needs, focusing on the global 21-cm signal is more practical initially, allowing measurements with a single antenna and paving the way for future, more detailed power spectrum studies.

The CosmoCube consists of various novel systems to generate a robust satellite described in the coming chapter. The experiments outlined in this paper extend to the characterization of a compact spectrometer utilizing the Xilinx ZCU111 evaluation board (Xilinx 2023), which houses the XCZU28DR-2FFVG1517E Radio Frequency System-on-Chip (RFSoC). The selection of this RFSoC for the CosmoCube project’s spectrometer represents a strategic decision, leveraging the device’s integration of RF Data Converters, Analog-to-Digital Converters (ADCs), and Digital-to-Analog Converters (DACs) within RFSoC FPGA architecture for precise and efficient spectral analysis for isolating the 21-cm signal from the foreground noises. The compact RFSoC technology suits the cube satellite format, reducing size and power requirements, simplifying operational complexity, and lowering mission costs. By minimizing size and power requirements, the mission can utilize smaller, less expensive launch vehicles and extend operational life, thereby lowering overall mission costs.

The RFSoC’s commercial availability and its broad adoption within engineering and research communities offer access to shared knowledge and resources, enhancing development processes. However, reliance on commercially available technology and community resources introduces dependencies on external developments, potentially constraining project-specific innovations. Additionally, the absence of a radiation-hardened package for this product poses challenges for space applications, necessitating careful management of these limitations. However, Davis et al. (2019) successfully characterized the radiation hardness of the ZCU111, focusing on its resistance to single-event upsets (SEU) and single-event latch-up (SEL) in a proton irradiation environment, using protons with energies ranging from 60 to 200 MeV. The findings confirm the device’s potential for applications in space, particularly in low Earth orbit, highlighting its resilience to radiation-induced errors and the effectiveness of its design modifications in managing latch-up events, with latch-ups occurring at an impressively low rate of approximately once every 90 yr. The findings confirm the device’s potential for applications in space. However, further testing is advised to fully understand whether its radiation resistance also holds in the harsher radiation environment of lunar orbit, especially regarding its high-speed analogue components.

Section 2 outlines the CosmoCube framework and lunar far side observations. Section 3 details the spectrometer characterization experiments. Section 4 evaluates FPGA capabilities for mission applicability. Section 5 concludes with final remarks.

Deploying a radio telescope on the Moon’s surface involves multiple challenges, such as uncertain lunar ground conditions and the ground spillover effect, which complicates signal detection. Using the finite difference time domain (FDTD) technique, Bassett et al. (2020) effectively characterized low-frequency radio wave propagation on the lunar far side. Building on this, Burns et al. (2021b) mapped the radio-quiet regions, enhancing the potential for precise observations from lunar missions and mitigating RFI from Earth. Despite these advancements, RFI from other lunar landers and orbiting satellites continues to pose significant challenges, as the effects of such interference are not fully understood due to the limited exploration of the Moon’s far side. The complexity of achieving a soft landing further complicates surface-based missions.

Given these challenges, space agencies’ plans to return to the Moon make lunar missions increasingly advantageous and popular among researchers. Leveraging the interest and resources directed towards lunar exploration can facilitate the deployment of advanced scientific instruments.

Deploying an orbiting satellite offers considerable advantages. Satellites provide enhanced mobility and flexibility, allowing for dynamic observation strategies without the limitations of a fixed position. Additionally, they carry a lower risk of environmental interference compared to surface instruments, which are susceptible to dust and extreme thermal conditions that can impair functionality and longevity. However, an orbital approach also has disadvantages, such as increased susceptibility to RFI from the lunar surface, limited observation windows per orbit, potential systematics caused by reflections from the lunar surface interfering with the direct signal, and communication delays with the payload. Consequently, while an orbital approach simplifies operational demands and proves more cost-effective and efficient for conducting lunar observations, these challenges must be carefully managed.

For satellite-based telescope operations, establishing a direct line of sight with Earth facilitates communication, eliminating the dependence on intermediary relay satellites required by far side landers. This direct transmission method simplifies data exchange and significantly boosts the mission’s overall efficiency.

To optimize the satellite’s performance during nighttime operations, when the 21-cm signal detection is most favourable due to minimal solar noise and maximum Earth’s occultation shielding from terrestrial RFI, careful planning of the orbital distance is critical, which set to be chosen in the range of 100–1000 km above the lunar surface. The integration of solar panels and precise sizing of the onboard battery ensure that the CosmoCube utilizes stored energy effectively. However, it is important to note that solar panels can also cause distortions in the EM field and beam of the instrument, necessitating careful design considerations. Additionally, having electronics in close proximity to the receiver requires extreme care in terms of shielding to prevent interference and maintain the integrity of the 21-cm signal detection. These operations necessitate a meticulous balance between energy harvest, storage, and usage, ensuring the satellite’s functions are supported through the lunar night. This balance is achieved by carefully calibrating power generation and consumption to within a specific margin, ensuring that the satellite remains operational even under the most challenging thermal and power conditions. Thermal analysis for a 12U satellite, where ‘12U’ refers to the satellite’s size being equivalent to 12 standard CubeSat units (each ‘U’ typically being a 10×10×10 cm cube), was carried out under three scenarios: high solar flux during daylight, low solar flux during daylight, and a lunar eclipse, with reference data from a report by NASA (2019). The lowest temperature recorded during the lunar eclipse was −112 C. The extreme temperature variations on the Moon demand a sophisticated thermal management system. This system is crucial to protect the satellite’s electronics and battery, maintain component temperatures within operational ranges, and ensure robust calibration of the system, ensuring that the 21-cm signal is accurately estimated from the captured data.

One of the earliest missions was the Soviet Union’s Luna 3 in 1959. Luna 3 was the first spacecraft to photograph the Moon’s far side, returning grainy but groundbreaking images that revealed a landscape very different from the familiar near side (Lipsky 1962). Another orbiter, Lunar Reconnaissance Orbiter (LRO), was developed by NASA in 2009, and the pictures are published online as open source (Tooley et al. 2010). China’s Chang’e-4 mission, launched in 2018, marked another significant milestone. Chang’e-4 was the first mission to land on the lunar far side, deploying a lander and a rover, Yutu-2, in the South Pole-Aitken Basin. This mission has provided detailed on-the-ground observations and measurements of the lunar far side, providing valuable data for lunar science and potential future manned missions (Li et al. 2019).

More recently, India’s Chandrayaan-2 mission (Sundararajan 2018), launched in 2019, attempted a soft landing near the lunar south pole, but the Vikram lander unfortunately crashed during its descent. Building on this experience, India successfully landed its Chandrayaan-3 mission near the lunar south pole in 2023, marking a significant achievement in lunar exploration (Indian Space Research Organisation 2023). Japan has also been active in lunar exploration with its OMOTENASHI mission, launched in 2022, which aimed to be the first Japanese lunar lander. However, the mission failed due to communication issues, resulting in an unsuccessful landing (Hashimoto et al. 2019). Russia’s Roscosmos also renewed its lunar exploration efforts with the launch of the Luna 25 mission in 2023, intended to land near the lunar south pole. However, the mission ended in a crash landing during descent, highlighting the challenges of lunar exploration (Mitrofanov et al. 2021). Another notable success was China’s Chang’e-5 mission in 2020, which not only landed on the Moon but also successfully returned lunar samples to Earth (Zhou et al. 2022). Although several missions have been made to the far side of the Moon as yet, none have specifically aimed to detect the 21-cm signal.

The CosmoCube mission parameters, as specified in Table 1, aims to detect the 21-cm hydrogen signal, emphasizing the necessity for precise detection across 0–128 MHz frequency bandwidth, which covers the science goal frequency range of 10 to 100 MHz. The channelizer’s bin width helps reduce the noise floor of the system whilst increasing the power consumption. Thus, a compromise was made to find an optimum value of 62.5 kHz. This will be detailed in the later chapters. The clock frequencies are carefully synchronized and chosen to facilitate the identification of potential signal components from external sources within our targeted frequency range.

As the response received at the antenna or the components in the front end does not have a flat response through our frequency of interest, a requirement of 0.1 dB is added.

The 21-cm signal is generated using GLOBALEMU (Bevins et al. 2021). The constraining power of the CosmoCube data set depends on the shape and depth of the 21-cm signal relative to the noise in the data. Precision constraints are placed on parameters such as star formation efficiency (), X-ray efficiency (), minimum virial circular velocity (), cosmic microwave background optical depth (), and minimum X-ray frequency () in a high signal-to-noise regime, as demonstrated in REACH experiment (Lera Acedo et al. 2022). This analysis is carried out using the Bayesian framework developed by Anstey, de Lera Acedo & Handley (2021). The confidence in recovering these signals, measured by the difference in Bayesian evidence, increases significantly when the thermal sensitivity reaches 10 mK or better.

Achieving this sensitivity across the 5–45 MHz range with a 0.1 MHz channel width requires approximately 1000 h of integration, as evaluated by the radiometer equation. This integration time is the minimum needed to accurately reduce thermal noise for reliable estimation of the 21-cm signal. With a mission duration of up to 3 yr, there is flexibility for further optimization to ensure the success of the observations.

The 10 mK limit restricts the ability to constrain certain physical parameters. Mondal & Barkana (2023) demonstrate the relative errors and limits on various parameters across different noise temperature levels, which increase with higher redshifts. The baryon density () and total matter density () can be reliably estimated in the bandwidth. In contrast, there is greater uncertainty in constraining the helium fraction (). Our aimed thermal sensitivity aligns with the difference between the two experiments, where the signal strength predicted by Planck’s measurement of the reduced Hubble constant (h) (Planck Collaboration VI 2020) is about 10 mK lower than that inferred from the SH0ES measurement (Riess et al. 2022) within the model.

Key considerations for the orbital altitude include the use of Earth occultation to minimize RFI, establishing reliable communication between the payload and Earth, and addressing the cost of satellite end-of-life disposal, which increases with orbit altitude due to the higher fuel or energy required for controlled re-entry. According to International Telecommunication Union (2013), man-made RFI sources radiate from up to 100 000 km from Earth’s centre. This creates a cone-shaped shielded zone on the far side of the Moon, extending about 6700 km from the lunar centre, with the Moon’s diameter being approximately 3500 km. Earth-based RFI observations by Yan et al. (2023) reported a maximum 2 dB increase in their measured spectrum of −147 , which includes sky and receiver signal between 6 and 20 MHz in the shadow of the Moon’s far side. This suppression of RFI aligns with the dynamic range requirement of around 80 dB to effectively study cosmological signals from the dark ages.

The highest sky brightness temperature within the bandwidth is around  K, approximately 70 dB above our targeted thermal sensitivity. While an 80 dB dynamic range is sufficient to enable the analysis of the dark ages signal from the brightest sky temperature, stronger RFI around the Moon, which is not included in this estimate, may require a greater dynamic range. The 80 dB estimate provides adequate headroom between the strongest sky signal and the targeted weakest measurement, 10 mK. Although achieving this dynamic range is feasible, achieving the 10 mK sensitivity will require rigorous calibration, a process currently under study. Future work will focus on calibrating the system with sufficient stability to maintain 10 mK sensitivity over extended periods.

The initial model of CosmoCube is shown in Fig. 2(a) for the deployed satellite structure and in Fig. 2(b) for the stowed satellite structure. To meet its operational energy requirements, the CosmoCube is equipped with solar panels and a battery pack designed to provide a continuous power supply for the duration of the mission. This setup ensures all satellite components receive regulated power for sustained optimal performance. The satellite’s orientation and stability in lunar orbit are meticulously controlled by altitude and thruster management systems, facilitating precise maneuverability and required elements to deorbit at the end of its lifecycle.

Central to the CosmoCube’s scientific payload is a radiometer, supported by a deployable science antenna for the 21-cm signal acquisition, an RF front end for initial signal processing, and a calibrator to enhance measurement accuracy. The stowed antenna is designed to fit in about 1U package during the launch. One of the elects of the deployed antenna is about 3 m long. Besides the bowtie, the other types of candidate antennas include dipole and blade dipole. However, this paper will not delve into the details of the antenna design, as it is still under development. Regardless, it is important to note that the presence of the satellite body and solar panels can significantly affect the beam shape by introducing distortions and reflections that alter the intended radiation pattern. These distortions can lead to inaccuracies in the 21-cm signal acquisition, potentially complicating data interpretation. Careful consideration and mitigation strategies, such as type of antenna, precise placement of the antenna relative to the satellite structure, and advanced EM modelling, will be crucial to minimize these effects.

This paper delves into the capability of the RFSoC FPGA, pictured in Fig. 3, for efficient and precise spectral analysis, which is essential for isolating the 21-cm signal from foreground noise. The compact design of the RFSoC is particularly beneficial for the cube satellite format of the CosmoCube project. This integration not only reduces the physical size and power requirements of the satellite but also cuts down on operational complexity and overall mission costs.

Fig. 4 illustrates CosmoCube’s front-end setup, featuring calibrators parallel to the antenna to simulate observations and generate various noise profiles. This setup, using a Dicke switch-based calibrator system similar to the one in a paper by Razavi-Ghods et al. (2023), adopts vector network analyser (VNA) principles for calibration. This includes input and output couplers with a switching mechanism for seamless calibration and detection mode transitions. A variable gain amplifier (VGA) compensates for non-linear gain responses from the antenna and other components, enhancing signal linearity within the measurement bandwidth. An anti-aliasing filter (AAF) is incorporated to meet Nyquist’s theorem, ensuring accurate signal sampling by avoiding aliasing.

For this setup, three ADCs and one DAC are utilized within the RFSoC. DAC generates waveforms for calibration purposes, whilst two ADCs measure power on the incident and reflected signals on the couplers to measure the reflection coefficients. The final ADC generates a spectrum by processing ADC samples through a channelizer. We have utilized Simulink blocks to design FPGA algorithms.

In the detection mode, the system operates with a single ADC active, while the calibration mode activates two extra ADCs and a DAC. The configuration of single ADC and single DAC is detailed in Fig. 5. In the receiving operation, the signal’s journey through the architecture starts with its capture by the XM500 Balun Board, followed by digitizing the signal via the ADC. Post-ADC, the signal undergoes decimation to reduce the data rate for more manageable processing while maintaining the integrity of the signal information. The Polyphase Filter Bank (PFB) then efficiently separates the signal into multiple frequency bands, optimizing the signal for the Fast Fourier Transform (FFT) process. The FFT block transforms the time-domain data into the frequency domain, facilitating the identification and analysis of specific frequency components. Following this transformation, data are temporarily stored in block RAM (BRAM), configured as first in first out (FIFO) for efficient data management. Following FFT, data are routed through buffers and direct memory access (DMA) for efficient data handling, eventually being stored in DDR4 memory. The processed data are then accessible for further analysis externally, completing the reception and initial processing phase, ensuring a comprehensive approach to cosmic signal detection and analysis.

The process of PFB involves segmenting a high-rate data stream into multiple lower rate streams using input commutators, enhancing manageability and reducing complexity. Each channel is processed by an FIR (finite impulse response) filter with varying coefficients to optimize signal integrity and minimize distortion. This setup manages spectral folding or aliasing when reducing sample rates, ensuring precise frequency band extraction. A subsequent FFT phase aligns and separates the baseband aliases, shifting signals from the time domain to the frequency domain for detailed analysis or further processing. This integrated approach significantly enhances both efficiency and performance in digital communication systems.

Using a look-up table (LUT) for pre-defined signal patterns, the DAC precisely converts digital signals into analogue form. These signals are then transmitted through the XM500 Balun Board to aid in system calibration. The waveform generation starts with the numerically controlled oscillator (NCO), which produces a precise frequency. This frequency is interpolated to enhance the signal-to-noise ratio (SNR) before being modulated and fed back into the DAC for final analogue conversion.

Given the importance of precise signal processing in our system, we carefully considered the trade-offs between floating-point and fixed-point arithmetic. Floating-point operations provide a wide range of values and precision, but they require more resources and have higher latency. Furthermore, floating-point numbers are prone to precision loss due to their limited representation of real numbers. This limitation becomes pronounced when dealing with large values, leading to information loss in significant digits. Conversely, fixed-point operations are more resource-efficient and have lower latency, although they have a limited range and precision. While it offers less dynamic range compared to floating-point arithmetic, because of the rounding errors inherent in fixed-point calculations. However, for our channelizer, where efficient resource utilization is crucial, fixed-point arithmetic is utilized due to its lower overhead. For the post-processing of the data, we worked with floating-point arithmetic on Matlab to plot the measurements.

An interpolated signal, when presented at a higher sampling rate, is an exact reproduction of the original signal. Upsampling a signal sampled at F to a higher sample rate (N*F) involves inserting N-1 zeros between each sample of the original signal. This process results in N replications of the original spectrum due to the creation of spectral images at multiples of the original sampling frequency. Low-pass filtering of the result helps to remove unwanted replications resulting in the preservation of the original signal at the required higher sample rate.

Various testing equipment was utilized to characterize the RFSoC for low frequency spectrometer design. The Keysight E8257D generated signals to assess the harmonic distortions and noise performance of the RFSoC ADC. The Keysight PNA-X was used to analyse the data generated by the RFSoC DAC, specifically measuring the spurious free dynamic range (SFDR) in spectrum analyser mode. Furthermore, the Keysight PNA-X was used to generate two-tone signals.

In the CosmoCube project, the ZCU111 RFSoC FPGA’s DAC setup with a sample rate of 2048 MSPS for 65536 samples per clock cycle. A 256 MHz clock frequency was chosen to cover the necessary band up to 128 MHz. Although our mission targets frequencies up to 100 MHz, the 128 MHz bandwidth provides a margin for signal processing and filtering, addressing potential out-of-band noise or interference. A higher ADC clock frequency helps avoid aliasing and accurately sample the signal, ensuring stable observation and acquirement of the spectrum with the channelizer. The 32-bit stream data width provides a significant dynamic range, ensuring the preservation of signal integrity. Since this exceeds the RFSoC ADC’s bit depth of 12-bit, it maintains data integrity and allows for additional data to be streamed concurrently.

The samples are transmitted to an external source at a data rate of 655 kbps. This is a relatively high speed, requiring substantial data storage in the payload before transmission to Earth. Assuming the payload is at 1000 km above the Moon, we have 43 min of data collection during Earth’s occultation, which is the area inside the cone-like shadow of the Moon. At a data rate of 655 kbps, this results in approximately 201 MB of data, which is significant. However, due to averaging within FPGA, this data will be reduced to below 4 MB per observation on the far side.

This section outlines the methodology for measuring the accuracy, efficiency, and overall performance of the RF data converters through a series of systematic tests. This analysis outlines testing methods for assessing the performance of these converters in capturing low-frequency signals from the dark ages. Accurate characterization ensures that the RFSoC meets the sensitivity and dynamic range required for studying cosmic phenomena, with performance parameters optimized to reflect the variations in signal properties across different redshift.

In conclusion, the CosmoCube instrument represents an advancement in lunar and space-based radio astronomy, particularly in exploring the faint 21-cm hydrogen line from the dark ages. By overcoming terrestrial limitations and harnessing innovative technologies such as the Xilinx RFSoC, which, while highly advanced, is not yet fully space-qualified but will undergo testing and can be placed in a tailored space-qualified hermetically sealed package, CosmoCube provides unprecedented sensitivity and resolution, offering new insights into the early Universe’s structure and evolution. Unlike the custom-built analogue components in systems like EDGES, REACH, and SARAS, the RFSoC offers a higher level of integration and availability of various sources in the firmware development, which is advantageous for the rapid and cost-effective development of the spectrometer. However, it requires careful consideration of its space-readiness, particularly in terms of radiation hardness and thermal management. Utilizing a channelizer in the spectrometer, we achieved an ENOB of approximately 11.5 and an NSD of around −152.5 dBFS Hz⁻¹, highlighting the system’s high precision and low noise performance across the frequency range of interest. Even with the exceptional performance showing only a 0.2 dB variation under extreme temperatures, thermal systems are still required to maintain stability, particularly for the calibration of the system. However, it is important to note that no receiver has yet been coupled to the system, which could introduce new challenges or alter its performance. The integration of the receiver may reveal additional complexities, requiring further adjustments to optimize signal integrity and overall system behaviour. Furthermore, the need for stringent filtering techniques was evident, as harmonic levels impacted data integrity. The implementation of specialized filters and characterization of these spurious signals will be critical in future refinements to reduce signal contamination and enhance the overall quality of the cosmological data collected by CosmoCube. Further analysis of power consumption will be made to optimize the balance between system performance and operational longevity, ensuring the mission’s sustainability and efficiency in the harsh conditions of space.